The “gospel” is from the study of certain log-concave conjectures on combinatorial problems. J. Huh [1]} adopted techniques from algebraic geometry to construct some special algebraic varieties which admit a log-concave sequence in homology group. A wide connection between log-concave sequence and Hodge theory [2]}, [3]} was introduced to prove log-concave conjectures in a unified manner.
Coincidentally, completely monotone functions also admit a log-concave characterization. It will be intriguing to see whether Huh's method work in the setting of completely monotone functions.
